Second answer first, to make what are called pretty permalinks, in your admin panel go to Settings > Permalinks - then choose "Custom structure" and paste this into the field beside it
/%postname%/ then "save changes" from the bottom of the page.
As for the first question by main page you mean the one that shows the blog posts I assume, do you mean you'd like to have a static page at playthissongloud.com then have the blog posts show on playthissongloud.com/blog/ ?
IF so after you've done the permalink change mentioned above go to Pages in your admin panel and create two new pages, one named "Home" and the other named "Blog"
then go to Settings > Reading - and beside where it says "Front page displays" choose "a static page" and select Home from the dropdown list for front page, and blog from the for posts page.
Go to playthissongloud.com hit refresh and you should be good.